With industrialization, the need for the design of building systems using a few prefabricated components has led to the search for new modular systems. Invariably, this search has led to building systems based on repetitive, or periodic, geometries where a unit or a cluster of units is translated (moved) in space in one, two or three directions. The economy of design, manufacturing, analysis, costing, and construction is built-in since only the basic module, and how this module fits with others, needs to be resolved in greater detail. There are design issues of overall organization and composition which require consideration, but the advantages of modularity are compelling. This type of thinking has led to the design of many periodic building systems, the most notable being space frames like Buckminster Fuller's "octet truss", Menringhausen's Mero system, Peter Pearce's universal node, and many others which are mostly design variations but retain the underlying geometry, symmetry and topology of a few types of periodic symmetries. Many of such periodic building systems have been in practice and have led to an upsurge of interest in the search for new and innovative geometries, new ways to define and organize architectural space, new structural systems and new ways to construct. There is a constant need to find new structures and configurations.
Among periodic geometries, regular (Platonic) and semi-regular (Archimedean) polyhedra have provided a basis for deriving various types of building systems. The works of the architects Tyng, Hecker, Safdie, Baer, Critchlow, Strutt, Giorgini and Gabriel are cited. Among the geometries using regular polygons (planar polygons with equal edges and angles), space labyrinths composed of regular faces are an attractive class of spatial configurations with interesting applications in various fields. Space labyrinths are a class of space structures which are characterized by a continuous infinite surface which divides space into two parts, inside and outside, without self-intersections. Periodic space labyrinths composed of planar regular polygons and having one one type of vertex, are known from the prior work of Petrie and Coxeter, and Burt et al where they were alternatively described as infinite polyhedra in such labyrinths, every vertex of the labyrinth is alike, i.e. the number and types of polygons meeting at every vertex is the same. Burt has proposed the use of his infinite polyhedra for very large spans on the kilometer scale, and has also suggested plate-type, cylindrical and spherical use of such labyrinths for architecture.
Prior related patents include U.S. Pat. No. 2,803,088 to J. A. Swann; U.S. Pat. No. 3,600,825 to P. Pearce; U.S. Pat. No. 3,632,147 to J. Finger; U.S. Pat. No. 3,91,360 to P. M. Baldwin; U.S. Pat. No. 3,974,600 to P. Pearce, U.S. Pat. No. 4,129,975 to R. J. Gabriel; and U.S. Pat. No. 4,183,190 to J. A. Bance.
This applications deals with new periodic labyrinths, also composed of regular faces, but having two types of vertices. The two types of vertices alternate with one another throughout the labyrinth, and the labyrinths are derived from regular and semi-regular polyhedra of tetrahedral, octahedral symmetries and prismatic. Such labyrinths are not known in prior art. Since the geometries of such labyrinths are new, applications based on these geometries will also be new. The labyrinths can be easily converted into "solid" space-fillings by filling in the open faces and open cells, thereby converting the labyrinth from a continuous surface into a close-packing of various polyhedra.
Both the labyrinths and the derived space-fillings provide a basis for novel architectural and building systems. Further, as described herein, the space labyrinths are composed of nodal polyhedra and connector polyhedra which can easily be converted into space frames composed of nodes and struts by elongating the connector polyhedra and developing suitable connection devices.
In addition to the field of architecture and design, the new geometries may be used at microscopic levels in the design of filters and sieves. Car filters, windows that "breathe", sieves for fluids, are candidate applications. Designed molecular sieves for chemical purification in industrial processes are other possibilities.